today in geometry… warm up: inscribed polygons stats for ch.10 quiz learning target : 10.5 you...
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TODAY IN GEOMETRY…
Warm up: Inscribed Polygons
STATs for Ch.10 Quiz
Learning Target : 10.5 You will find the measures of angles inside or outside of a circle
Independent practice
WARM UP: Find the value(s) of the variable(s).
1. 2. 3.
HOW DID YOU “SHAPE” UP??Results for ALL of my Geometry classes:
GRADE NUMBER OF STUDENTS WHO TOOK THE CH.10 QUIZ (16 pts.)
1ST PERIOD 3RD PERIOD 5TH PERIOD 6TH PERIOD TOTAL
A 15 18 18 17 68B 3 5 3 6 19C 0 0 0 0 0D 2 3 0 0 5F 2 0 4 0 6
Avg. 14.11 14.52 14.26 15.09 14.50
THEOREM-CHORDS AND TANGENTS: If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of the intersected arc.
2 1
𝐴
𝐵𝐶
PRACTICE:
PRACTICE:
12
(210 ° )=𝟏𝟎𝟓° 2 (98 ° )=𝟏𝟗𝟔° 2 (80 ° )=𝟏𝟔𝟎°
INTERSECTING LINES AND CIRCLES: If two lines intersect a circle, there are three places where the lines can intersect:
𝑶𝑵 h𝑡 𝑒𝑐𝑖𝑟𝑐𝑙𝑒
𝑰𝑵𝑺𝑰𝑫𝑬 h𝑡 𝑒𝑐𝑖𝑟𝑐𝑙𝑒
𝑶𝑼𝑻𝑺𝑰𝑫𝑬 h𝑡 𝑒𝑐𝑖𝑟𝑐𝑙𝑒
INSIDE ANGLE THEOREM: If two chords intersect inside a circle, then the measure of each angle is one half the sum (addition) of the measures of the arcs intercepted by the angle and its vertical angle.
𝐶𝐵
𝐴
𝐷
12
EXAMPLE:
PRACTICE: Find the value of x.
Use Inside Angle Theorem:
EXAMPLE: Find the value of y.
Find the value of the missing angle: Use Inside Angle Theorem:
2 ∙ ∙2
PRACTICE: Find the value of x.
Find the value of the missing angle: Use Inside Angle Theorem:
2 ∙ ∙2
25 °137 °
𝑥 °43 °
OUTSIDE ANGLE THEOREM: If two lines intersect outside a circle, then the measures of the angle formed is one-half the difference (subtract) of the measures of the intercepted arc.
𝐶
𝐵
𝐴
1
𝑅
𝑄𝑃
2
𝑌
𝑋𝑊3𝑍
EXAMPLE:
EXAMPLE: Find the value of x.
Find the missing arc measure: Use Outside Angle Theorem:
110°
EXAMPLE: Find the value of a.
Use Outside Angle Theorem:
∙22 ∙
PRACTICE: Find the value of x.
Use Outside Angle Theorem:
∙22 ∙
EXAMPLE: Find the value of x.
Use Outside Angle Theorem:
∙22 ∙
EXAMPLE: Find the value of x.
Use Outside Angle Theorem:
∙22 ∙
61 °(5 𝑥−1)°(10 𝑥+1)°
PRACTICE: Find the value of x.
Use Outside Angle Theorem:
∙22 ∙
5 4 °(5 𝑥+14)°(13 𝑥−6)°
HOMEWORK #5:
Pg. 683: 3-13
If finished, work on other assignments:
HW #1: Pg. 655: 3-20, 24-26, 30HW #2: Pg. 661: 3-14, 17, 23HW #3: Pg. 667: 3-15HW #4: Pg. 676: 3-16 Pg. 679: 40-46